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Superconductivity Current

In superconductivity, a simply connected body cannot sustain a steady surface current without an external magnetic field. In spherical coordinates, the equation DY = 0 has solutions expressed as powers of r, implying conditions where dY/dr is constant and equal to zero at boundaries. This indicates that the magnetic field H must also be zero, thereby prohibiting the existence of steady currents on such bodies. In contrast, for a simply connected body in the presence of an external H-field, a magnetic moment emerges, revealing the complexity of magnetic behavior in superconductors.

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Superconductivity Current

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  1. Superconductivity Current Section 54

  2. A simply connected body can have no steady surface current in the absence of an external magnetic field.

  3. In spherical coordinates, DY = 0 has solutions that are powers of r: ra, where a can be positive or negative. If dY/dr is zero at both r = a and r = infinity, the only possible value of a is zero. Then dY/dr = 0 at all r, or Y = constant, giving H = 0. An H-field of this kind cannot exist -> there can be no steady current on a simply connected body.

  4. For a simply-connected body in an external H-field, a magnetic moment M appears

  5. Multiply connected superconductor f is many valued

  6. Zero, since H=B outside and divB = 0.

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